This renewal application proposes continued work on (1) new or improved quantitative methods for assessing the effects of exposures to one or more environmental toxicants, expecially carcinogens (2) application of these methods to data from human studies and animal experiments. Methods include the use of (i) quantiative models (e.g., the multistage theory of cnacer induction, proportional hazard models) to obtain biologically relevant parameters and summary statistics; (i) nonparametric and robust statistical procedures (e.g., repeated sampling procedures) to remove bias in small samples, to obtain nonparametric confidence intervals for measures of association, to temper the effects of extreme or anamalous observations, and to deal with missing data. As a dividend of this research, PhD students in the Department of Statistics at Stanford University will receive training and experience in analyzing human and animal data from studies in environmental toxicology.